According to Sky Sports, Manchester United were interested in signing Senegal international winger Mane, while Kenya international defensive midfielder Wanyama was wanted by Tottenham Hotspur, as reported by The Mirror.
Former Liverpool defender Carragher believes that keeping the duo at St. Mary’s Stadium was important for Southampton.
“Wanyama is a great protection for the back four, although he has missed Schneiderlin and those two were vital for the great defensive record Southampton had last year.”
Carragher also gave his verdict on Virgil van Dijk, who joined Southampton from Scottish Premiership giants Celtic in the summer.
“Losing Toby Alderweireld was a blow for Saints and it was important to get someone in like Van Dijk to play alongside Jose Fonte,” said the Englishman.
“I haven't seen loads of Van Dijk but he has a reputation for scoring goals and his job will be to help Southampton keep clean sheets as they did last season.”
Southampton enjoyed a successful 2014-15 Premier League campaign, as they finished as high as seventh in the league table.
Ronald Koeman’s side have not made a great start to this season, but they should remain optimistic.
The Saints will face United at St. Mary’s Stadium in the Premier League on Sunday afternoon.
Southampton will head into the encounter on the back of a goalless draw with West Bromwich Albion away from home at The Hawthorns.